IPCTRAIN - Editorial

PROBLEM LINK:

DIFFICULTY:

Easy

PREREQUISITES:

Greedy,Heap

PROBLEM:

You have an upcoming camp. There are N trainers. The camp runs for D days.Each day,there can be at most one lecture. The ith trainer arrives on day Di and then stays till the end of the camp. He also wants to teach exactly Ti lectures. For each lecture that a trainer was not able to teach,his sadness level will be increased by Si.
You are the main organizer of the contest. You want to find minimum total sadness of the trainers.

EXPLANATION:

Let's assign our trainers starting from the first day of the camp. At each day adding arriving trainers to our set of trainers.

Each day should be assigned to only one trainer, it's obvious that we should assign the trainer with maximum sadness to this lecture, so our set (container) should be a heap sorting trainers by their sadness value. In fact we should know also the number of days each lecturer wants to serve in, so we take the lecturer with maximum sadness from our heap and decrease his demand by 1. In case he still has lectures he would like to do, we keep him in the heap, otherwise we just pop him out.

After finishing all days, some teachers may have some remaining lectures they wanted to teach but we couldn't find such days for them. Let's denote the number of lectures the ith trainer couldn't teach by remi So our answer would be :

$answer = \sum_{i=1}^{i=N} rem_i * S_i$

AUTHOR'S AND TESTER'S SOLUTIONS:

AUTHOR's solution: Will be found hereTESTER's solution: Will be found hereEDITORIALIST's solution: Will be found here

If I solve the above question using heaps as stated, then on popping out the trainer which doesn't have any lecture remaining and at the very same time maintaining the sort would require the complexity O(n).
On the other hand if we just extract him from the heap and heapify using time complexity O(lg n) would disturb the sort. How do i proceed?

Declare t.sadness as long instead of int or use type casting as sadness+=1LL * t.lectures * t.sadness; - because product of 2 int is stored in the int type and then the overflowed result is stored in sadness.